Gaussian beams and caustic avoidance in gravitational optics

TL;DR

This paper introduces a covariant Gaussian beam framework in gravitational optics, enabling modeling of light propagation from finite sources while avoiding caustics and singularities, with applications to cosmological distances.

Contribution

The work develops a covariant Gaussian beam method applicable in any spacetime, extending wave-based light propagation models in gravitational fields and avoiding caustic singularities.

Findings

Gaussian beams can model finite sources in gravitational optics.

The method avoids caustic singularities in light propagation.

Application demonstrated in Barriola-Vilenkin monopole spacetime.

Abstract

In this study, we consider a beam summation method adapted from the semiclassical regime of quantum mechanics to study the classical properties of thin light bundles in gravity. In Newtonian paraxial optics, this method has been shown to encapsulate the wave properties of the light beams. In our case, the wave function assigned to the light bundle can be viewed as a coarse-grained description that captures information about the dynamics of superposed bundles within the geometric optics regime. We investigate two solutions of the null bundle wave function that differ by their origin: (i) a point source and (ii) a finite source. It is shown that while the wave function in the point source case contains the same information as the standard thin null bundle framework, the finite source case corresponds to a Gaussian beam. The novel aspect of this work arises from our geometric construction of covariant Gaussian beams, which can be applied in any spacetime. Additionally, the effects of a finite source on cosmological distances are discussed. With this framework, one can model light propagation from coherent sources while avoiding the mathematical singularities of the standard thin null bundle formalism. We explicitly demonstrate the caustic-avoidance property of Gaussian beams in the analytically tractable example of a Barriola-Vilenkin monopole spacetime.